PC

02.21.13SOME 4.7 AND 4.8 STUFF

SOLVE A RADICAL eQUATION 4.7

Lesson Overview 4-7A

Try #2101 kk

Answer: 25.5025 = k

22

101 kk

10012

kk

10011 kkkk

100)1(2 2 kkkk

100212 2 kkk

2

21012 kkk

2

22

2

2101

k

kk

22 5.50 kkk 22 10125.2550 kkkk

k10025.25500

k5025.25

You have to square TWICE

SOLVE A RADICAL INEQUALITY 4.7

UNDERSTANDING DOMAINS IS IMPORTANT HERE… TO DO THE ALGEBRA RIGHT

953 x

solution

3

76

3

5

x

Work for…..

953 x

Therefore

3

76

3

5

x

8153 x763 x

3

76x

But the square root can’t have a negative under it , so solve

053 x53 x

3

5xand

Pre-Calculus

Section 4.8• Modeling Real-World Data with Polynomial

Functions

Lesson Overview 4-8A

WHAT KIND OF POLYNOMIAL?

LOOK FOR TURNS IN THE DATA. IN A POLYNOMIAL THE NUMBER OF

TURNS IN THE GRAPH IS ONE LESS THAN THE DEGREE

SOME TIMES THE TURNS CAN BE VERY SUTTLE.. OR EVEN POINTS OF INFLEXION

USE OF CALCULATOR

OUR CALCULATOR IS ONLY PREPROGRAMED TO DEAL WITH 4TH DEGREE POLYNOMIALS..

ANY THING HIGHER AND WE NEED TO USE A METHOD INVOLVING SYSTEMS OF EQUATIONS AND MATRIX METHODS TO FIND.

EXAMPLE

USE the calculator to find a polynomial function to model the set of data.

YOU NEED TO SEE THE SCATTERPLOT TO HAVE A SENSE OF THE GRAPH BEFORE YOU GO TO THE REGRESSIONS.

Look at the scatter plot and decide which type of polynomial seems to the best.

Then do the appropriate regression.Linear, quadratic, cubic, or uartic ( the calculator has its limits high degree polynomials would require other methods …) Remember the correlation coefficient, r ??

x -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5f(x) -22.0 -7.9 0.0 3.5 4.1 2.9 2.1 2.5 5.8 14.1

Waste Management: the average daily amount of waste generated by each person in the USA is given below. This includes all waste such as industrial wastes, demolition waste and sewage.

Year 1980 1985 1990 1991 1992 1993 1994 1995 1996 2001

Pounds of Waste perPerson per day

3.7 3.8 4.5 4.4 4.5 4.5 4.5 4.4 4.3 4.4

a.) What polynomial function could be used?b.) use the model to predict the amount of waste for 2010c.) according to the model if and when will the waste per day drop below 3.0?

HwHW: pg 255 #1, 12-14, 18, 20, 24, 29-31, 36, 45 And pg 262 #8-11, 14, 19, 21, 23, 24

Test on Monday

Tomorrows assignment will bePg 267 # 11, 12, 14-16, 19, 20, 23-25, 28-30, 34, 35, 43 (use table and graph feature of calc), 44-47, 50-52, 54-58 If >80% done then = 100%, if >70% = 90% , if >60% = 80%, etc.